As I said previously, many believe Jesus was living in Capernaum by the time Luke began his record of Jesus’ public ministry (cf. Luke 4:23).  Nevertheless, whether Jesus was visiting his hometown of Nazareth or living there, he went into the synagogue and was probably asked by the ruler or president of the synagogue to read from the Scriptures and teach from them that Sabbath day (Luke 4:16). Synagogues were the center of Jewish life in the first century AD. They not only served as centers for prayer and worship, but often for formal education for local Jewish families, as well. Indeed, they functioned as courtrooms for the local sanhedrin (not to be confused with the supreme Sanhedrin at Jerusalem), and punishment was administered there in the local synagogue (Deuteronomy 25:3; cf. Mark 13:9; 2Corinthians 11:24).
The passage Jesus read was Isaiah 61:1-2a, and seems to have been marked out for him by the officer of the synagogue, responsible for maintaining the lectionary passages. It happened to be a Messianic passage, and, of course, its use for that Sabbath would have been known to any educated Jew who made himself aware of the reoccurrences of those passages. The use of the lectionary would cause the passages to be repeated either every year at the same time or every three years, depending upon whether an annual or a triennial cycle was in use during the 1st century AD. So, it isn’t as though, because Jesus didn’t choose the passage himself, he would be unaware that Isaiah 61:1-2a would be read that particular Sabbath. He would have been aware, and probably chose to be present in his hometown synagogue for its reading (assuming a Capernaum residence), because, whether or not he was chosen to read and teach from the passage, the discussion that would follow the reading would have permitted Jesus to make his point about himself. In other words, he would have been able to speak about the passage, whether or not he was chosen by the ruler of the synagogue to read and teach that Sabbath day.
That the passage is Messianic seems evident from what the rabbis claimed concerning Isaiah 11:2). Notice:
The Messiah-as it is written, And the spirit of the Lord shall rest upon him, the spirit of wisdom and understanding, the spirit of counsel and might, the spirit of knowledge of the fear of the Lord. And shall make him of quick understanding in the fear of the Lord. (Babylonians Talmud; Sanhedrin 93b – emphasis mine)
A comparison can be made from Isaiah 11:1-2, where a clear reference to the Messiah is made, and by considering Isaiah 42:1 (the Servant in whom the Lord delights), and Isaiah 59:20-21 (the Redeemer who comes to Zion), and Isaiah 61:1-2a. All these passages refer to the same person, and each Scripture concludes that the Spirit of the Lord rests upon the one under consideration. The context of the use of the clause “the Spirit of the Lord” shows that person has been anointed (meaning Messiah) by God. Therefore, when Jesus began his teaching from the passage by saying: “This day this Scripture is fulfilled in your ears” (Luke 4:26), he was saying to everyone present that he – Jesus – was the Messiah, and “the Spirit of the Lord” was actually upon himself—i.e. Jesus. This was a bold claim, and he was immediately challenged.
 Matthew 9:10, 13:1, 36; 17:24-25; Mark 9:33.
 Most scholars who embrace the use of the Jewish lectionary in the 1st century AD are uncertain of the use of the triennial cycle during this period. Its use would be more complex, and there is some doubt that it was composed by the time of Jesus’ days.
 The fact that Jesus is challenged at every point in these three chapters (i.e. 4-6) seems to support my understanding that Luke’s three temptations in Luke 4:1-13 are acted out in Galilee in 4:14 to the end of chapter 6. The wilderness Luke mentions in Luke 4:1 is rather a wilderness of people without spiritual understanding (Ezekiel 20:35).